1. Field of the Invention
The present invention relates to finite impulse response (FIR) filters and, more particularly, to FIR filters as they are applied to audio loudspeakers or other devices having a frequency response.
2. Description of the Related Art
An FIR type of digital filter has a finite impulse response in that it approaches zero in a finite number of sample intervals. In contrast, an infinite impulse response (IIR) filter has internal feedback and may continue to respond indefinitely. FIR filters have several advantages over IIR filters, including being inherently stable, requiring no feedback, and being capable of being linear or complex phase.
A basic form of an FIR filter may be provided by the following difference polynomial equation which defines how the input signal x[n] is related to the output signal y[n]:y[n]=b0x[n]+b1x[n−1]+ . . . +bNx[n−N]wherein bi are the filter coefficients. N is known as the “filter order.” An Nth-order filter has (N+1) terms on the right-hand side.
Another possible approach to defining the order of a polynomial is that the order is the highest order power in the polynomial, or alternatively, the polynomial's polynomial degree. For example, the polynomial P(x)=anxn+ . . . +a2x2+a1x+a0 is of order n, wherein n is greater than two (two being the highest other power of x that is shown in the equation).
FIR filters, because of their finite length, may exhibit problems correcting magnitude and phase at low frequencies, such as below 300 Hz. The frequency at which the FIR filter loses resolution is a function of the DSP sampling rate and the FIR filter order. This is related to the time-frequency uncertainty principle Δt·Δf=1 where Δt is an uncertainty in time and Δf is an uncertainty in frequency. Consequently, loudspeaker-room acoustic equalization may be difficult to achieve with FIR filters at low frequencies.
What is neither disclosed nor suggested in the art is a loudspeaker system that overcomes the problems and limitations described above. More particularly, what is neither disclosed nor suggested is a loudspeaker system employing an FIR filter that performs well at low frequency.